Patients undergoing marrow transplantation procedures as treatment for hematologic maligancy or marrow failure experience a predictable and discrete period of agranulocytosis associated with a high incidence of severe bacterial infection. Bacterial infections in many of these patients have been treated with granulocyte transfusions from normal donors. The benefits of this form of therapy cannot be objectively evaluated in a critical situation demanding all forms of potentially useful therapy. Experience with this method of treatment has permitted the design of a study comparing the incidence and severity of infection in two randomly derived groups of patients. All patients will be undergoing marrow transplantation as part of the treatment of leukemia or marrow failure. One group will receive daily granulocyte transfusions during the period of agranulocytosis between marrow ablation and satisfactory peripheral function of the engrafted marrow.